“With Britain’s entry into the EEC,” barked an early 1970s advert, “Centre Point, London, offers an unrivalled opportunity to organisations with imagination to occupy this spectacular office complex.” How times change. Now, with Britain’s impending exit from the EU, the same building offers an unrivalled opportunity for individuals wishing to spend £1.8m on a one-bedroom flat or £55m on a penthouse, the first of whom have been gradually moving in since last Christmas. A Crossrail station at its base will whisk owners from Tottenham Court Road to Heathrow airport in 28 minutes and thence to the new global opportunities promised by Brexiters.

Meanwhile, nine miles west of Centre Point’s central location, the celebrated former Hoover factory, whose colonnaded art deco billboard of a facade merges ancient Karnak with American roadside industry, is also turning into flats. For there’s an entropy in the contemporary property business, its own second law of thermodynamics, which states that eventually everything becomes residential.

The newly built Centre Point in 1966. Photograph: Peter King/Getty Images

These two white edifices, the temple and the tower, have something in common. Both were deplored by Nikolaus Pevsner, the architectural historian and postwar cataloguer of British architecture who made deploring into a one-man, quasi-nationalised industry. The Hoover, for him, was a “modernistic atrocity”, Centre Point “coarse in the extreme”. Both buildings, decried for their commercial vulgarity, have now inveigled their way into public and official affection. Spun around in the great washing machine of taste, both are now listed as buildings of architectural interest.

Centre Point, completed in 1966, has a special status in cultural history, for the fact that it stood empty for years while its owner, Harry Hyams, tried to find the one big corporation that would take it at the rents he wanted. It was claimed that the developer kept it purposely unoccupied for accounting reasons, as he could watch his paper profits grow as property values shot up. Hyams, a publicity-shy man who once wore a Mickey Mouse mask to a shareholders’ meeting to avoid being photographed, took successful legal action against such claims, but empty his tower nonetheless was.

At a time when, as now, there was seen to be a housing crisis, Centre Point managed to unify the Tory minister Peter Walker and the folk group Lindisfarne in opposing its sterile, antisocial pursuit of profit. The former attacked this “incredible scandal”. “Your madness is making a machine of everyone,” went the latter’s 1972 single All Fall Down, which featured the tower on its sleeve. Architectural reviews were more varied. Not everyone shared Pevsner’s scorn: some critics scented swinging London in its slender profile and zigzag rhythms. Neither Hyams nor his pipe-smoking architect, Colonel Richard Seifert, was exactly Mick Jagger or Marianne Faithfull, but you can see what these observers were thinking.

It is indeed London’s most stylish tower, even now, when, in quantity if not quality, there is so much competition. Broad on its two convex faces and miraculously thin at its ends, it has the merit of changing in proportion as it appears from different parts of the city. It tapers towards the top, like a classical column. Its skilful and bold structure, by the engineer Wilem Frischmann, is worn on the outside, in the form of that zigzag lattice, precast with a concrete mix of almost marble-like whiteness. The tower occupies its singular spot with confidence and bravura, terminating Oxford Street and calling across Fitzrovia to its equally idiosyncratic contemporary, the BT Tower. It has presence, its mass energised by the design’s devotion to angles other than 90 degrees.

Centre Point is the outcome of particular forms of talent, not all of them concerned primarily with beauty: Hyams’s as a developer, for example. It grew from Seifert’s special skill at working the planning system to his clients’ advantage, in this case giving the local authority a traffic gyratory system that they wanted in return for unexpected height. Seifert’s design partner, George Marsh, whose name is attached to a majority of the practice’s most memorable buildings, borrowed liberally from the great buildings of the recent past to give Centre Point its distinctive look. The profile owes much to Gio Ponti’s Pirelli tower in Milan, the expressive concrete to the mature work of Marcel Breuer. You can call it homage, or copying, but it works.

Cynical and expedient though it partly was, Centre Point had architectural qualities – form, composition, detail, depth, light and shadow – that are hard to find in most speculative buildings, then as now. So it is welcome that it should be given a new life by the developer Almacantar and the architectural practice Conran and Partners in an updated version of Seifertian louche luxury. A pedestrianised open space, to the designs of another practice, Mica, will open in phases from this summer.

The worst part of Seifert’s design was always the gyratory system that the planners saw as its main benefit, which, together with some wilfully mean pavements, made for an obnoxious and dangerous public space. The revamp loses some of the dynamism and distinctiveness of the old, but it’s preferable not to be asphyxiated and run over.

The Hoover factory, now known as the Hoover building, never reached Centre Point’s heights of controversy, but when it opened in 1933 in the nascent suburb of Perivale, it was still seen as a dangerous manifestation of an arterial-road Americana that the Town and Country Planning Act of 1947 would eventually stamp out. Like Centre Point, it combines stasis and motion, with the venerable forms of ancient Egypt repurposed to attract the attention of drivers on the roaring A40.

It, too, has been set to music, although more affectionately than Centre Point, in Elvis Costello’s Hoover Factory of 1980. “Must have been a wonder when it was brand new,” he carolled. And it has always been a delight, for its powerful horizontals offset by insistent verticals, for the exuberant ornament that plays off its solemn columns, for its absolute indifference to stylistic propriety, which allowed its architects Wallis Gilbert and Partners to throw Bauhaus glazing, expressionist corner windows and Native American forms into the eclectic mix. Its colours too: its sunny white concrete, the hopeful minty green of its steel window frames, the outbursts of red and rich blue in its glazed bricks.

“One of these days”, as Costello sang, it’s “gonna be all the rage in those fashionable pages”. And here it is, its value enhanced by the shocking demolition in 1980 of the nearby Firestone factory, also by Wallis Gilbert and Partners, over a bank holiday weekend. (Its owners wanted to pre-empt the Firestone’s probable listing.) The Hoover building is now in its second reincarnation, having been taken over by Tesco in the 1980s. Its less glamorous rear buildings were replaced by a superstore that still stands. Its front, used for offices by the retail giant, is now apartments, laid out to the designs of the engineering and architecture practice Interrobang.

The most interesting thing about Interrobang’s conversion, a light timber frame designed to minimise loading on the existing structure, is sadly not visible. It would have been nice to keep a sense of this, as if installing an inside-out Amish village in the old factory, but the conventions of the residential property market don’t allow for such adventure. What you get instead are flats of proportions and spatial complexity that come from their adjustment to the old fabric.

There is some weirdness – the noise from the road and from Tesco deliveries means you mostly can’t open windows and have to rely on a ventilation system for fresh air – but the spaces are still livelier and richer than you’d get in a new building.

Centre Point makes for nice flats too (as they should be for the price): long and slightly curving glass walls combined with the reassuring depth of the structure. This makes one grateful for the listing of relatively modern buildings, eccentric though the system sometimes is. As the rest of the planning system gets ever more flaccid, listing at least obliges architects to come up with non-standard designs and developers to pay them to do so.

Engineer Wilem Frischmann: ‘I just tried to do things differently’

The pioneering engineer of Centre Point looks back on the London landmark’s construction and the new type of building it ushered in

The engineer Wilem Frischmann, now aged 87 and still working, was not yet 30 when he designed the structure of Centre Point in central London. He says the site was made so complicated by pre-existing sewers and tube tunnels that no one had thought it possible to build much more than a single storey there – “only some shops”.

Wilem Frirschmann, c1966.

“When I grew up,” says Frischmann, “I was told you can’t build tower blocks on clay” – the stuff on which London stands – so he made a point of showing that you could.

“If it hadn’t worked then, I would have been dead,” he continues. But it did work. “That’s how I made friends with [Centre Point architect] Richard Seifert – I did 50 more buildings with him.” The success of the structure made property developer Harry Hyams “into the richest man in Britain”, asserts Frischmann.

Frischmann’s method was to drill close-packed piled foundations into the ground (he inspected the holes himself, got stuck in one and had to spend the night there until it was discovered how to get him out). The tower above is then unusually light, using thin floor slabs and the system of external structural elements that are the building’s signature. Precast in Portland, Dorset, and trucked to the site by night, these enabled the tower to rise at a rate of a storey a week. Their concrete was exceptionally strong, and its steel reinforcement has not suffered from the sort of corrosion that often forces structures of Centre Point’s age to be demolished.

Frischmann, a man unafraid to point out his achievements, is most proud of the glazed walls of a horizontal box that is a bridge between the tower and a lower block, over what was until recently a busy road. This, he says, is the first use of structural glass – panels that support themselves without the help of frames. It has become commonplace in sleek modernism since. How did he come up with the idea? “I just tried to do things differently,” he says.